Master Equation: Biological Applications and Thermodynamic Description

It is well known that many realistic mathematical models of biological systems, such as cell growth, cellular development and differentiation, gene expression, gene regulatory networks, enzyme cascades, synaptic plasticity, aging and population growth need to include stochasticity. These systems are not isolated, but rather subject to intrinsic and extrinsic fluctuations, which leads to a quasi equilibrium state (homeostasis). The natural framework is provided by Markov processes and the Master equation (ME) describes the temporal evolution of the probability of each state, specified by the number of units of each species. The ME is a relevant tool for modeling realistic biological systems and allow also to explore the behavior of open systems. These systems may exhibit not only the classical thermodynamic equilibrium states but also the nonequilibrium steady states (NESS). This thesis deals with biological problems that can be treat with the Master equation and also with its thermodynamic consequences. It is organized into six chapters with four new scientific works, which are grouped in two parts: (1) Biological applications of the Master equation: deals with the stochastic properties of a toggle switch, involving a protein compound and a miRNA cluster, known to control the eukaryotic cell cycle and possibly involved in oncogenesis and with the propose of a one parameter family of master equations for the evolution of a population having the logistic equation as mean field limit. (2) Nonequilibrium thermodynamics in terms of the Master equation: where we study the dynamical role of chemical fluxes that characterize the NESS of a chemical network and we propose a one parameter parametrization of BCM learning, that was originally proposed to describe plasticity processes, to study the differences between systems in DB and NESS.

Activity and mechanisms of action of novel organosulfur derivatives of the HDAC inhibitor Valproic Acid in human experimental models of non-small-cell lung cancer

Non-small-cell lung cancer (NSCLC) represents the leading cause of cancer death worldwide, and 5-year survival is about 16% for patients diagnosed with advanced lung cancer and about 70-90% when the disease is diagnosed and treated at earlier stages. Treatment of NSCLC is changed in the last years with the introduction of targeted agents, such as gefitinib and erlotinib, that have dramatically changed the natural history of NSCLC patients carrying specific mutations in the EGFR gene, or crizotinib, for patients with the EML4-ALK translocation. However, such patients represent only about 15-20% of all NSCLC patients, and for the remaining individuals conventional chemotherapy represents the standard choice yet, but response rate to thise type of treatment is only about 20%. Development of new drugs and new therapeutic approaches are so needed to improve patients outcome. In this project we aimed to analyse the antitumoral activity of two compounds with the ability to inhibit histone deacethylases (ACS 2 and ACS 33), derived from Valproic Acid and conjugated with H2S, in human cancer cell lines derived from NSCLC tissues. We showed that ACS 2 represents the more promising agent. It showed strong antitumoral and pro-apoptotic activities, by inducing membrane depolarization, cytocrome-c release and caspase 3 and 9 activation. It was able to reduce the invasive capacity of cells, through inhibition of metalloproteinases expression, and to induce a reduced chromatin condensation. This last characteristic is probably responsible for the observed high synergistic activity in combination with cisplatin. In conclusion our results highlight the potential role of the ACS 2 compound as new therapeutic option for NSCLC patients, especially in combination with cisplatin. If validated in in vivo models, this compound should be worthy for phase I clinical trials.

Turbulence models in the atmospheric boundary layer under convective conditions

In this work a modelization of the turbulence in the atmospheric boundary layer, under convective condition, is made. For this aim, the equations that describe the atmospheric motion are expressed through Reynolds averages and, then, they need closures. This work consists in modifying the TKE-l closure used in the BOLAM (Bologna Limited Area Model) forecast model. In particular, the single column model extracted from BOLAM is used, which is modified to obtain other three different closure schemes: a non-local term is added to the flux- gradient relations used to close the second order moments present in the evolution equation of the turbulent kinetic energy, so that the flux-gradient relations become more suitable for simulating an unstable boundary layer. Furthermore, a comparison among the results obtained from the single column model, the ones obtained from the three new schemes and the observations provided by the known case in literature ”GABLS2” is made.

Transposable elements dynamics in taxa with different reproductive strategies or speciation rate

In recent years the advances in genomics allowed to understand the importance of Transposable Elements (TE) in the evolution of eukaryotic genomes. In this thesis I face two aspects of the TE impact on the in the animal kingdom. The first part is a comparison of the dynamics of the TE dynamics in three species of stick-insects of the Genus Bacillus. I produced three random genomic libraries of 200 Kbps for the three parental species of the taxon: a gonochoric population of Bacillus rossius (facultative parthenogenetic), Bacillus grandii (gonochoric) and Bacillus atticus (obligate parthenogenetic). The unisexual taxon Bacillus atticus does not shows dramatic differences in TE total content and activity with respect to Bacillus grandii and Bacillus rossius. This datum does not confirm the trend observed in other animal models in which unisexual taxa tend to repress the activity of TE to escape the extinction by accumulation of harmful mutations. In the second part I tried to add a contribute to the debate initiated in recent years about the possibility that a high TE content is linked to a high rate of speciation. I designed an evolutionary framework to establish the different rate of speciation among two or more taxa, then I compared TE dynamics considering the different rates of speciation. The species dataset comprises: 29 mammals, four birds, two fish and two insects. On the whole the majority of comparisons confirms the expected trend. In particular the amount of species analyzed in Mammalia allowed me to get a statistical support (p<0,05) of the fact that the TE activity of recently mobilized elements is positively related with the rate of speciation.

Pricing in stochastic-local volatility models with default

In recent years is becoming increasingly important to handle credit risk. Credit risk is the risk associated with the possibility of bankruptcy. More precisely, if a derivative provides for a payment at cert time T but before that time the counterparty defaults, at maturity the payment cannot be effectively performed, so the owner of the contract loses it entirely or a part of it. It means that the payoff of the derivative, and consequently its price, depends on the underlying of the basic derivative and on the risk of bankruptcy of the counterparty. To value and to hedge credit risk in a consistent way, one needs to develop a quantitative model. We have studied analytical approximation formulas and numerical methods such as Monte Carlo method in order to calculate the price of a bond. We have illustrated how to obtain fast and accurate pricing approximations by expanding the drift and diffusion as a Taylor series and we have compared the second and third order approximation of the Bond and Call price with an accurate Monte Carlo simulation. We have analysed JDCEV model with constant or stochastic interest rate. We have provided numerical examples that illustrate the effectiveness and versatility of our methods. We have used Wolfram Mathematica and Matlab.

A simple and novel method to monitor breathing and heart rate in awake and urethane-anesthetized newborn rodents

Rodents are most useful models to study physiological and pathophysiological processes in early development, because they are born in a relatively immature state. However, only few techniques are available to monitor non-invasively heart frequency and respiratory rate in neonatal rodents without restraining or hindering access to the animal. Here we describe experimental procedures that allow monitoring of heart frequency by electrocardiography (ECG) and breathing rate with a piezoelectric transducer (PZT) element without hindering access to the animal. These techniques can be easily installed and are used in the present study in unrestrained awake and anesthetized neonatal C57/Bl6 mice and Wistar rats between postnatal day 0 and 7. In line with previous reports from awake rodents we demonstrate that heart rate in rats and mice increases during the first postnatal week. Respiratory frequency did not differ between both species, but heart rate was significantly higher in mice than in rats. Further our data indicate that urethane, an agent that is widely used for anesthesia, induces a hypoventilation in neonates whilst heart rate remains unaffected at a dose of 1 g per kg body weight. Of note, hypoventilation induced by urethane was not detected in rats at postnatal 0/1. To verify the detected hypoventilation we performed blood gas analyses. We detected a respiratory acidosis reflected by a lower pH and elevated level in CO2 tension (pCO2) in both species upon urethane treatment. Furthermore we found that metabolism of urethane is different in P0/1 mice and rats and between P0/1 and P6/7 in both species. Our findings underline the usefulness of monitoring basic cardio-respiratory parameters in neonates during anesthesia. In addition our study gives information on developmental changes in heart and breathing frequency in newborn mice and rats and the effects of urethane in both species during the first postnatal week.

Analytische Ableitungen der Energie für den "Equation-of-Motion-Coupled-Cluster"-Ansatz zur Berechnung von Ionisationspotentialen

In der vorliegenden Arbeit wird die Theorie der analytischen zweiten Ableitungen für die EOMIP-CCSD-Methode formuliert sowie die durchgeführte Implementierung im Quantenchemieprogramm CFOUR beschrieben. Diese Ableitungen sind von Bedeutung bei der Bestimmung statischer Polarisierbarkeiten und harmonischer Schwingungsfrequenzen und in dieser Arbeit wird die Genauigkeit des EOMIP-CCSD-Ansatzes bei der Berechnung dieser Eigenschaften für verschiedene radikalische Systeme untersucht. Des Weiteren können mit Hilfe der ersten und zweiten Ableitungen vibronische Kopplungsparameter berechnet werden, welche zur Simulation von Molekülspektren in Kombination mit dem Köppel-Domcke-Cederbaum (KDC)-Modell - in der Arbeit am Beispiel des Formyloxyl (HCO2)-Radikals demonstriert - benötigt werden.rnrnDer konzeptionell einfache EOMIP-CC-Ansatz wurde gewählt, da hier die Wellenfunktion eines Radikalsystems ausgehend von einem stabilen geschlossenschaligen Zustand durch die Entfernung eines Elektrons gebildet wird und somit die Problematik der Symmetriebrechung umgangen werden kann. Im Rahmen der Implementierung wurden neue Programmteile zur Lösung der erforderlichen Gleichungen für die gestörten EOMIP-CC-Amplituden und die gestörten Lagrange-Multiplikatoren zeta zum Quantenchemieprogramm CFOUR hinzugefügt. Die unter Verwendung des Programms bestimmten Eigenschaften werden hinsichtlich ihrer Leistungsfähigkeit im Vergleich zu etablierten Methoden wie z.B. CCSD(T) untersucht. Bei der Berechnung von Polarisierbarkeiten und harmonischen Schwingungsfrequenzen liefert die EOMIP-CCSD-Theorie meist gute Resultate, welche nur wenig von den CCSD(T)-Ergebnissen abweichen. Einzig bei der Betrachtung von Radikalen, für die die entsprechenden Anionen nicht stabil sind (z.B. NH2⁻ und CH3⁻), liefert der EOMIP-CCSD-Ansatz aufgrund methodischer Nachteile keine aussagekräftige Beschreibung. rnrnDie Ableitungen der EOMIP-CCSD-Energie lassen sich auch zur Simulation vibronischer Kopplungen innerhalb des KDC-Modells einsetzen.rnZur Kopplung verschiedener radikalischer Zustände in einem solchen Modellpotential spielen vor allem die Ableitungen von Übergangsmatrixelementen eine wichtige Rolle. Diese sogenannten Kopplungskonstanten können in der EOMIP-CC-Theorie besonders leicht definiert und berechnet werden. Bei der Betrachtung des Photoelektronenspektrums von HCO2⁻ werden zwei Alternativen untersucht: Die vertikale Bestimmung an der Gleichgewichtsgeometrie des HCO2⁻-Anions und die Ermittlung adiabatischer Kraftkonstanten an den Gleichgewichtsgeometrien des Radikals. Lediglich das adiabatische Modell liefert bei Beschränkung auf harmonische Kraftkonstanten eine qualitativ sinnvolle Beschreibung des Spektrums. Erweitert man beide Modelle um kubische und quartische Kraftkonstanten, so nähern sich diese einander an und ermöglichen eine vollständige Zuordnung des gemessenen Spektrums innerhalb der ersten 1500 cm⁻¹. Die adiabatische Darstellung erreicht dabei nahezu quantitative Genauigkeit.

Asymptotics for Marginal Generalized Linear Models With Sparse Correlations

Marginal generalized linear models can be used for clustered and longitudinal data by fitting a model as if the data were independent and using an empirical estimator of parameter standard errors. We extend this approach to data where the number of observations correlated with a given one grows with sample size and show that parameter estimates are consistent and asymptotically Normal with a slower convergence rate than for independent data, and that an information sandwich variance estimator is consistent. We present two problems that motivated this work, the modelling of patterns of HIV genetic variation and the behavior of clustered data estimators when clusters are large.

Efficiency of the Sieved-NPMLE in CAR-Missing Data Models

We consider nonparametric missing data models for which the censoring mechanism satisfies coarsening at random and which allow complete observations on the variable X of interest. W show that beyond some empirical process conditions the only essential condition for efficiency of an NPMLE of the distribution of X is that the regions associated with incomplete observations on X contain enough complete observations. This is heuristically explained by describing the EM-algorithm. We provide identifiably of the self-consistency equation and efficiency of the NPMLE in order to make this statement rigorous. The usual kind of differentiability conditions in the proof are avoided by using an identity which holds for the NPMLE of linear parameters in convex models. We provide a bivariate censoring application in which the condition and hence the NPMLE fails, but where other estimators, not based on the NPMLE principle, are highly inefficient. It is shown how to slightly reduce the data so that the conditions hold for the reduced data. The conditions are verified for the univariate censoring, double censored, and Ibragimov-Has'minski models.

Evaluating Prediction Rules for t-Year Survivors With Censored Regression Models

Suppose that we are interested in establishing simple, but reliable rules for predicting future t-year survivors via censored regression models. In this article, we present inference procedures for evaluating such binary classification rules based on various prediction precision measures quantified by the overall misclassification rate, sensitivity and specificity, and positive and negative predictive values. Specifically, under various working models we derive consistent estimators for the above measures via substitution and cross validation estimation procedures. Furthermore, we provide large sample approximations to the distributions of these nonsmooth estimators without assuming that the working model is correctly specified. Confidence intervals, for example, for the difference of the precision measures between two competing rules can then be constructed. All the proposals are illustrated with two real examples and their finite sample properties are evaluated via a simulation study.

Relationship between glomerular filtration rate and the adipokines adiponectin, resistin and leptin in coronary patients with predominantly normal or mildly impaired renal function

BACKGROUND: Due to their molecular weight, it is possible that the adipokines adiponectin, resistin and leptin accumulate when glomerular filtration rate (GFR) is decreased. In reduced renal clearance, altered serum concentrations of these proteins might affect cardiovascular risk. The objective of the study was to investigate the relationship between adipokine concentrations and GFR. METHODS: The association between GFR, as determined by the abbreviated MDRD equation, and the concentrations of the adipokines adiponectin, resistin and leptin was assessed in a cohort of coronary patients (n=538; 363 male, 165 female). After calculation of correlations between GFR and adipokine concentrations, the association was further assessed by analysis of covariance following adjustment for age, gender, BMI, presence of type 2 diabetes, presence of hypertension, history of smoking as well as for serum lipid concentrations. RESULTS: Mean GFR in our study population was 68.74+/-15.27 ml/min/1.73 m(2). 74.3% of the patients had a GFR >60 ml/min/1.73 m(2), 24% of the patients had a GFR between 30 and 60 ml/min/1.73 m(2), and 1.7% of the patients had a GFR <30 ml/min/1.73 m(2). There were significant inverse correlations between adiponectin (r=-0.372; p<0.001), resistin (r=-0.227; p<0.001) and leptin (r=-0.151; p=0.009) concentrations and GFR. After multivariate adjustment, the associations remained significant for adiponectin and resistin. Subgroup analysis in patients with GFR >60 ml/min/1.73 m(2) showed a significant correlation between GFR and adiponectin as well as leptin concentrations. However, after adjustment, these associations no longer were significant. CONCLUSIONS: There is an independent association between GFR and the serum concentrations of adiponectin and resistin. However, this association is not present at GFR >60 ml/min/1.73 m(2). This finding suggests that adipokine concentrations in mildly impaired and normal renal function are influenced by factors other than GFR.